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Abstract

Nonlinear photonic-crystal microresonators offer unique fundamental ways of enhancing a variety of nonlinear optical processes. This enhancement improves the performance of nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic ultrafast integrated optical devices. Here, we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal microcavities. First, we discuss a system in which this enhancement has been successfully demonstrated both theoretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we show how nonlinear photonic crystal cavities can be also used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of materials can be strongly modified via the so-called Purcell effect, present in the resonant cavities under study.

Figures (7)

Sketch of a system composed by an optical resonator coupled symmetrically to both an input and output ports. ωc is the corresponding resonant frequency and Γ is the width of the resonance. Pin and Pout label the incoming and outgoing powers through the structure, respectively. Inset shows the typical linear transmission spectrum corresponding to this system.

(a) Evolution of the transmission spectra through the system sketched in Fig. 1 when the refractive index of the resonator is increased by δn. As can be seen in this panel, δn shifts the original resonant frequency of the cavity ωc (dashed line) towards the frequency of the external illumination ωp (blue dashed line). (b) Dependence of Pout/Pin as a function of the outgoing power for Δ=3 (see text for details on this magnitude). (c) Same function as (b) but this time Pout is plotted as a function of Pin for several values of Δ. Dotted lines display the unstable branches of the hysteresis loop for each case.

(a) Photonic crystal implementation of the system sketched in Fig. 1. The PhC is made by a periodic two dimensional distribution of high dielectric rods (εH=12.25, yellow regions in the figure) in a low-ε background (εL=2.25). The rods have a radius of r=0.25a. A point defect, introduced by increasing the radius of the central rod to r=0.33a, is symmetrically coupled to two single mode PhC waveguides on the left and right. The electric field pointing into the page is depicted with positive (negative) values in red (blue). (b) Computed dependence of the output power (Pout) as a function of the input power (Pin) for the structure shown in panel (a) when the central rod is assumed to be made by a nonlinear Kerr-like material. Green line displays the results obtained from a perturbation theory analysis while the blue dots correspond to the result of a nonlinear FDTD simulation. Dashed lines represent the unstable branch of the bistable loop.

Schematic diagram of waveguide-cavity system. Input light from a waveguide (left) at one frequency ω1 is coupled to a doubly-resonant cavity (with resonances at ω1 and ω2, with respective lifetimes Q1 and Q2) and converted to a cavity mode at another frequency ω2 by a χ(2) process. The converted light is radiated back into the waveguide at both frequencies.

Plot of conversion efficiency Pω2out/Pin (black), and reflection Pω1out/Pin vs. Pin for the schematic geometry in Fig. 4 (Here Pωin/out denotes input/output power at frequency ω). The maximum conversion efficiency is achieved at the expected critical power P0. To compute this figure, we have chosen conservative modal parameters ω1=0.3 2πc/a, Q1=104, Q2=2Q1, 1/VHG≈10-5a-3 (where a is the characteristic length scale of the system, see Ref. [35] for further details on this calculation).

A 7×7 square lattice of dielectric rods (ε=12.25) in air, with a single defect rod in the middle. On top of the dielectric structure outlined in black, the Ez field is plotted, with positive (negative) values in red (blue). A small region of nonlinear material, e.g., a CdSe nanocrystal, with transition frequency ωelec, is placed in the defect rod.

(a) Numerical calculation of the enhancement of SE for the set-up in Fig. 6, given by the ratio of the rate of emission in the PhC, T-11,purcell, divided by the emission rate in vacuum, T-11,vac. (b) Kerr enhancement η≡Reχ(3)purcell/Reχ(3) vac as a function of electronic transition frequency (ωelec) for a system of dielectric rods in air, with the parameter values listed in the text.